ECS204 Signals and Systems (Jan-Apr 2026)
Lectures: Tuesday, Thursday, Friday (11 : 00 − 11 : 55) [L1, LHC]
Pre-requisites: None
Course modules:
1. Signals:
(a) Signal classification (analog-digital, energy-power, even-odd, periodic-aperiodic, deterministic-random etc.), standard signals (unit step, unit impulse, ramp, exponential, sinusoids), transformations of the independent variable (shifting, scaling, reversal).
(b) Discrete exponential functions and their properties.
(c) Discrete unit step and impulse signals and their properties.
2.Systems:
(a) System classifications (linearity, time invariance, memory, analog/digital, continuous /discrete time, causality).
(b) Convolution (discrete and continuous time).
(c) System properties via the impulse response (causality, memory, stability, invertibility, unit step response).
3. Fourier series of periodic functions:
(a) History of Fourier series, Euler to Fourier.
(b) Response of LTI systems to complex exponentials and Fourier series representation of continuous time periodic signals.
(c) Fourier series representation of sawtooth, square and triangular waves.
(d) Properties of Fourier series and examples.
(e) Convergence of Fourier series and Gibbs phenomena.
(f) Fourier series and LTI systems; filtering.
4. Fourier Transform:
(a) Introduction of the continuous time Fourier transform by taking the limit of a periodic signal (i.e. making it aperiodic).
(b) Fourier transforms of periodic signals.
(c) Properties of continuous time Fourier transforms.
(d) Convolution property of Fourier transforms.
(e) Brief introduction to sampling theorem.
5. Laplace Transform:
(a) Introduction to Laplace transform; region of convergence.
(b) Inverse Laplace transform.
(c) Properties of Laplace transforms, initial/final value theorems.
(d) Laplace transforms and LTI systems, causality/stability.
(e) Laplace transforms and block system diagrams.
(f) Unilateral Laplace transform and initial value problems.
Books:
Signals and Systems: Oppenheim, Willsky, and Nawab (2nd Edition).
Principles of Linear Systems and Signals: B.P. Lathi (2nd Edition).
Grading (absolute): 30% for 2 Quizzes, 30% Mid-Sem exam, 40% End-Sem exam.